Autorotation flight control system

ABSTRACT

The present invention provides computer implemented methodology that permits the safe landing and recovery of rotorcraft following engine failure. With this invention successful autorotations may be performed from well within the unsafe operating area of the height-velocity profile of a helicopter by employing the fast and robust real-time trajectory optimization algorithm that commands control motion through an intuitive pilot display, or directly in the case of autonomous rotorcraft. The algorithm generates optimal trajectories and control commands via the direct-collocation optimization method, solved using a nonlinear programming problem solver. The control inputs computed are collective pitch and aircraft pitch, which are easily tracked and manipulated by the pilot or converted to control actuator commands for automated operation during autorotation in the case of an autonomous rotorcraft. The formulation of the optimal control problem has been carefully tailored so the solutions resemble those of an expert pilot, accounting for the performance limitations of the rotorcraft and safety concerns.

The United States Government has a paid-up license in this invention andthe right in limited circumstances to require the patent owner tolicense others on reasonable terms as provided for by the terms of NASAContracts NAS2-02008 and NAS2-02096 awarded by the NASA, Ames ResearchCenter, Moffett Field, Calif.

FIELD OF THE INVENTION

The present invention relates to a methodology using optimal control forapplication to the time critical maneuvering of dynamic systemsincluding vehicles such as rotorcraft. The methodology is implemented ina computer-based system for calculating and displaying optimal-controlinput commands to a human-operator for autorotation flight control of arotorcraft and is adapted for training helicopter pilots in a flightsimulator on safe maneuvering in time critical situations involvingtotal engine power failure (autorotation) and partial power failure. Themethodology can also be used for automated guidance of dynamic systemsincluding vehicles such as rotorcraft in time critical maneuveringsituations and in an automated system that will provide the highestlikelihood of a safe landing if the pilot is incapacitated or if thevehicle is unmanned.

BACKGROUND ART

A series of analytical and experimental work has been done to understandand describe the nature of the dynamics and pilot's recovery techniquesin rotorcraft's power failure. Johnson (Ref. 1) analytically describedthe dynamics of rotorcraft's autorotation. Lee (Refs. 2, 3), Zhao (Refs.4-6), Carlson (Refs. 7-10), and Okuno (Refs 11, 12) investigated theapplication of constrained optimization to investigate the safeoperational envelopes for autorotation and reduced-power situations fora variety of rotorcraft ranging from single-engine (OH-58A, Refs. 2-3)to multi-engine, for instance UH-60A and Bell M430, (Refs. 4-6, 8, 11,12, 10) to tilt-rotor (Refs. 7, 9, 10). Johnson (Ref. 1) investigatedthe autorotation of a helicopter from a hover, and Lee (Refs. 2, 3)refined the problem formulation by adding inequality constraints forthrust and vertical velocity. Lee postulated that the “avoid” regions inthe height-velocity (H-V) restriction curve could be substantiallyreduced if optimal pilot inputs were used during autorotation.References 2 and 3 used a point-mass model of an OH-58A helicopter andthe cost function was a weighted sum of the squared horizontal andvertical components of the helicopter velocity at touchdown. Thepoint-mass model had two degrees-of-freedom (vertical and horizontalvelocity) with an additional rotor speed degree-of-freedom. The inputs(horizontal and vertical thrust) required to minimize the cost functionwere computed using nonlinear optimal control theory. The correlationbetween flight data and the optimal results established the adequacy ofthe use of a point mass model in the optimal helicopter landing study(Ref. 2, 3). References 2 and 3 also validated the method by comparingthe optimal profiles (helicopter states and controls) with availableautorotation flight-test data for the OH-58A. A unique feature of theRefs. 2 and 3 formulation was the addition of path inequalityconstraints on components of both the control and the state vectors. Thecontrol variable inequality constraint is a reflection of the limitedamount of thrust that is available to the pilot in the autorotationmaneuver without stalling the rotor. The state variable inequalityconstraint is an upper bound on either the vertical sink rate of thehelicopter or the rotor angular speed during descent. “Slack” variableswere employed to convert these path inequality constraints into pathequality constraints. The resultant two-point boundary-value problemwith path equality constraints was successfully solved using theSequential Gradient Restoration Algorithm (SGRA). With bounds on thecontrol and state vectors, the optimal solutions obtained willrealistically reflect the limitations of the helicopter and its pilot.The model in Ref. 2 and 3 used assumed zero-wind, vertical plane motion,and zero-slip flight. Zhao (Ref 4-6) extended the work by Lee (Ref. 2,3) to investigate the takeoff and landing trajectories of a dual-enginehelicopter in the event of a single engine failure. Zhao also used theSGRA for computing the optimal trajectories and used differentconstructions for the objective (cost) function to investigate optimalprofiles for continued and rejected landings and takeoffs in the eventof a single engine failure. In addition to touchdown velocity,horizontal distance was also included in the objective function toexamine the implications of an engine failure on the safe return andlanding or continued flight of the helicopter. A point-mass model of aUH-60A helicopter was used in this work with improvements to the modelto include engine torque and a ground-effect model. Carlson (Ref. 7-10)launched from the previous body of work and used optimal control theoryto investigate the unsafe (avoid) regions of the H-V envelope in theevent of single-engine failure as well as complete engine failuresituations in a civil tiltrotor aircraft and a dual engine helicopter. Arelatively sophisticated three degree-of-freedom (vertical andhorizontal velocity and pitch attitude) rotorcraft model was used withan added rotor speed degree-of-freedom and a non-linear aerodynamicmodel of the XV-15 tilt-rotor aircraft and the Bell M430 helicopter. Animportant contribution of the Refs. 7-10 work was the improvement in theoptimization method. The Ref. 7-10 work demonstrated that the SGRAoptimization method was not robust in the face of more complex problemformulations. The Refs. 7-10 work successfully implemented a directmethod of optimization (Ref. 13) where the continuous two-point boundaryvalue problem is discretized into a parameter optimization problem. Theoptimization used a well-established and mature nonlinear programmingalgorithm that is commercially available (Refs. 14, 15). The presentinvention applies a similar strategy to compute the optimal controlinputs and resulting flight path for rotorcraft autorotation.

LIST OF REFERENCES

-   (1) Wayne Johnson, “Helicopter Optimal Descent and Landing after    Power Loss,” NASA Technical Memorandum, NASA™ 73244, May 1977.-   (2) Allan Y. Lee, “Optimal Landing of a Helicopter in Autorotation,”    Ph.D. Dissertation, Stanford University, July 1985.-   (3) Allan Y. Lee, Arthur E. Bryson, Jr., and William S. Hindson,    “Optimal Landing of a Helicopter in Autorotation,” Journal of    Guidance, Vol. 11, No. 1, pp 7-12, January-February 1988.-   (4) Y. Zhao and R. T. N. Chen, “Critical Consideration for    Helicopters During Runway Takeoffs,” Journal of Aircraft, Vol. 32,    No. 4, pp 773-781, July-August 1995.-   (5) Y. Zhao, Ali A. Jhemi, and R. T. N. Chen, “Optimal Vertical    Takeoff and Landing Helicopter Operation in One Engine Failure,”    Journal of Aircraft, Vol. 33, No. 2, pp 337-346, March-April 1996.-   (6) R. T. N. Chen and Y. Zhao, “Optimal Trajectories for the    Helicopter in One-Engine-Inoperative Terminal-Area Operations,”    Presented at the FVP Symposium on “Advances in Rotorcraft    Technology”, Ottawa, Canada, May 1996.-   (7) Eric B. Carlson, “Optimal Tiltrotor Aircraft Operations During    Power Failure,” Ph.D. Dissertation, University of Minnesota, July    1999.-   (8) Eric B. Carlson, “An Analytical Methodology for Category A    Performance Prediction and Extrapolation,” Presented at the American    Helicopter Society 57th Annual Forum, Washington, D.C., May 9-11,    2001.-   (9) Eric B. Carson and Y. Zhao, “Prediction of Tiltrotor    Height-Velocity Diagrams Using Optimal Control Theory,” Journal of    Aircraft, Vol. 40, No. 5, pp 896-905, September-October 2003.-   (10) Ali A. Jhemi, Eric B. Carlson, Y. Zhao, and R. T. N. Chen,    “Optimization of Rotorcraft Flight Following Engine Failure,”    Journal of American Helicopter Society, Vol. 49, No. 2, pp 117-126,    April 2004.-   (11) Y. Okuno and Keiji Kawachi, “Optimal Takeoff of a Helicopter    for Category A V/STOL Operation,” Journal of Aircraft, Vol. 30, No.    2, pp 235-240, March-April 1993.-   (12) Y. Okuno, Keiji Kawachi, Akira Azuma, and Shigeru Saito,    “Analytical Prediction of Height-Velocity Diagram of a Helicopter    Using Optimal Control Theory,” Journal of Guidance, Vol. 14, No. 2,    pp 453-459, March-April 1991.-   (13) C. R. Hargraves and S. W. Paris, “Direct Trajectory    Optimization Using Nonlinear Programming and Collocation,” Journal    of Guidance, Vol. 10, No. 4, pp 338-342, July-August 1987.-   (14) Philip E. GILL, Walter MURRAY, Michael A. SAUNDERS, and    Margaret H. Wright, “USER'S GUIDE FOR NPSOL 5.0,” Technical Report    SOL 86-1, Stanford University, Revised Jul. 30, 1998.-   (15) Philip E. GILL, Walter MURRAY, and Michael A. SAUNDERS, “USER'S    GUIDE FOR SNOP Version 6.0,” Stanford University, December 2002.-   (16) Watts, Joseph C., Gregory W. Condon, and John V. Pincavage,    “Height-Velocity Test, OH-58A Helicopter,” USAASTA Project No.    69-16, June 1971.-   (17) Dooley, L. W. and Yeary, R. D., “Flight Test Evaluation of the    High Inertia Rotor System,” USARTL-TR-79-9, June 1979.-   (18) E. N. Bachelder and Bimal L. Aponso “Using Optimal Control for    Rotorcraft Autorotation Training,” Proceedings of the American    Helicopter Society 59th Annual Forum, Phoenix, Ariz., May 6-8, 2003.

SUMMARY DISCLOSURE OF THE INVENTION

The autorotation capability of helicopters following engine powerfailure is a unique feature that can provide a means for executing asafe landing. However, the autorotation maneuver can requireconsiderable skill and proficiency that is not normally acquired throughnominal flight training.

In most autorotation training, pilots receive in-flight instruction onautorotation technique using initial conditions that are well outside ofthe hover-velocity (H-V) restriction curve of the helicopter flown—andthe engine remains powered. Additionally, the entry conditions(altitude, relative wind direction, and especially airspeed) are usuallyconsistent from one practice autorotation to another (within model andinstructor). Autorotation training in a simulator is an infrequent eventfor most pilots, and even the best simulators poorly reproduce the cuesrequired during an actual autorotation. The primary utility ofsimulators as an autorotation training aid, therefore, is to develop aproficient instrument scan procedure. The likelihood of a successfulautorotation performed under actual instrument conditions, however, isextremely remote. Clearly rotary pilots have few resources to help themtrain toward and maintain autorotation proficiency, so that theautorotation is usually regarded as a ‘take what comes and pray’maneuver.

In one aspect the present invention comprises the application of areal-time trajectory optimization method for guiding a mannedrotorcraft, an autonomous unmanned rotorcraft, or a remote operator ofan unmanned rotorcraft, through an autorotation in the event of partialor total loss of power. The invention provides for safe landing of sucha rotorcraft. Further, successful autorotations may be performed fromwell within the manufacturer's designated unsafe operating area of theheight-velocity profile of a rotorcraft or helicopter by employing thefast and robust optimal algorithm of the present invention. Theinvention applies nonlinear constrained optimal control theory to solvefor a vehicle's trajectory and the required control inputs to accomplisha successful autorotation. The guidance algorithm of the presentinvention generates optimal trajectories and control commands via thedirect-collocation optimization method, solved using a commerciallyavailable nonlinear programming problem solver. The control inputscomputed by optimal control formulation are collective pitch andaircraft pitch, which are easily manipulated by an onboard or remotepilot or converted to collective and longitudinal cyclic commands in thecase of an autonomous unmanned rotorcraft. The formulation of theoptimal control problem has been carefully tailored to enable thesolutions to resemble those of an expert pilot, accounting for theperformance limitations of the rotorcraft as well as safety concerns. Apreview of the commanded flight control input suite, which isdynamically updated as the vehicle state changes in time, is provided tothe pilot of a manned or remotely operated unmanned rotorcraft throughan intuitive visual display. In the case of an autonomous unmannedrotorcraft the present invention provides commands for control motiondirectly through a link to a conventional commercially availableautopilot.

In another aspect the present invention comprises a novel trainingmethodology and a system that takes advantage of automation's potentialas a high-speed decision aid and the strengths of human patternrecognition and conditioning. In this embodiment the invention iscoupled with a flight simulator to train pilots across a range ofrotorcraft platforms. Using the invention's command preview display andother display functions incorporated with a flight simulator a pilottrainee should be able to execute numerous maneuvers previouslyconsidered outside the operational envelope, in addition to performing‘standard’ emergencies with a high degree of control consistency andaccuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a depiction of a single rotor helicopter.

FIGS. 2 a and 2 b depict a Frasca International Bell 206 Flight TrainingDevice (FTD).

FIG. 3 is a block diagram depicting the interface between the optimalguidance and the FTD.

FIG. 4 is a Height-Velocity diagram for the Bell 206L-4 HelicopterResults.

FIG. 5 is a diagram depicting the Automated autorotation flightconditions evaluated.

FIG. 6 is a diagram depicting the touchdown ground-speed and sink-rate(light weight condition).

FIG. 7 is a diagram depicting the touchdown ground-speed and sink-rate(medium and heavy weight conditions).

FIG. 8 is a diagram depicting a time history for selected flight andcontrol parameters for simulated automatic autorotation from 200 ft/0kts; light weight condition (2900 lbs).

FIG. 9 is a diagram depicting a time history for selected flight andcontrol parameters for simulated automatic autorotation from 400 ft/0kts; light weight condition (3100 lbs).

FIG. 10 is a diagram depicting a time history for selected flight andcontrol parameters for simulated automatic autorotation from 20 ft/70kts; light weight condition (3085 lbs).

FIG. 11 is a diagram depicting a time history for selected flight andcontrol parameters for simulated automatic autorotation from 300 ft/60kts; light weight condition (3085 lbs).

FIG. 12 is a diagram depicting a time history for selected flight andcontrol parameters for simulated automatic autorotation from 400 ft/0kts; heavy weight condition (4440 lbs).

FIG. 13 is a diagram depicting a schematic illustration of a firstembodiment of the current invention adapted for training rotorcraftpilots on a flight simulator.

FIG. 14 is a diagram depicting a system schematic of the currentinvention.

FIG. 15 is a diagram depicting a description of guidance visual displaycomponents as a part of the current invention.

FIG. 16 is a diagram depicting a schematic illustration of a secondembodiment of the current invention adapted for automatically guiding amanned or unmanned rotorcraft.

FIG. 17 is a diagram depicting a schematic illustration of a thirdembodiment of the current invention adapted as a computer-based trainingdevice for autorotation/reduced-power emergency flight.

INDUSTRIAL APPLICABILITY OF THE INVENTION AND MODES FOR CARRYING OUT THEINVENTION

The present invention is directed to systems for autorotation flightcontrol, and in particular to the computer implemented system thatprovides directions for controlling the flight of helicopters or ofother rotorcraft upon loss of power to maximize the likelihood of a safelanding. The present invention may take the form of various embodiments,such as for example in a system adapted for a flight simulator forsingle engine, single rotor helicopters, a flight simulator for multipleengine, single or multiple rotor helicopters or a flight simulator forother rotorcraft. Embodiments of the present invention may also take theform of control systems for use in real working helicopters or otherrotorcraft (as opposed to a simulator). When adapted for use in pilotedworking aircraft, the system is be adapted to provide displayinformation for controlling the flight of the aircraft to maximize thelikelihood of safe landing and/or is be adapted to provide automaticcontrol inputs to the aircraft for such landings. When adapted for usein drones or other aircraft without pilots the system is be adapted forproviding remote display for remote control of the aircraft and/or forautomatic control inputs to the aircraft.

In the following description, numerous specific details are set forth toprovide a more thorough description of embodiments of the invention. Inlight of the present disclosure, other embodiments will become obviousto those of ordinary skill in the art and such embodiments are withinthe scope of the present invention. It will be apparent, however, to oneskilled in the art, that the invention may be practiced without thesespecific details. In other instances, well known features have not beendescribed in detail so as not to obscure the invention. Except as notedherein, common components and connections, identified by commonreference designators function in like manner.

In the description and included mathematical expressions the symbolsused have the definitions or meanings stated in the following key tonomenclature:

a rotor blade two-dimensional lift curve slope (rad⁻¹) C_(P) powercoefficient C_(T) thrust coefficient (C_(x), C_(z)) (horizontal,vertical) component of thrust coefficient c_(d) ₀ mean profile dragcoefficient of rotor blades f_(e) equivalent flat plate area forfuselage (ft²) f_(G) ground effect factor f_(I) induced velocity factorg gravitational acceleration (ft/s²) (h, d) (vertical, horizontal)position (ft) H_(hub) rotor hub height when helicopter is on the ground(ft) I_(R) polar moment of inertia of the main rotor blade (slug-ft²) Jcost function K_(ind) induced power factor m mass of helicopter (slugs)P_(S) available shaft power (lbf · ft/s) P_(res) residual shaft power(lbf · ft/s) R main rotor radius (ft) t_(f) estimated flight time (s)(u, w) (horizontal, vertical) velocity components (ft/s) α tip pathplane angle (rad) γ weighting factor in cost function δ_(c) collectivepitch angle position (rad) δ_(col) normalized collective pitch angleposition δ_(cyc) normalized longitudinal cyclic position η helicopterpower efficiency factor λ rotor inflow ratio μ rotor advance ratio ρ airdensity (slugs/ft³) σ rotor solidity ratio τ_(p) turboshaft engine timeconstant (s) θ aircraft pitch angle (rad) Ω main rotor angular speed(rpm) ν rotor induced velocity (ft/s) ν_(h) induced velocity at hover(ft/s) ( )₀ initial values at engine failure ( )_(max) maximum valueallowed ( )_(min) minimum value allowed ( )_(ref) reference value ()_(nom) reference valueThe Rotorcraft Model

The rotorcraft equations of motions are detailed below.

$\begin{matrix}{{m\;\overset{.}{w}} = {{m\; g} - {{\rho\left( {\pi\; R^{2}} \right)}\left( {\Omega\; R} \right)^{2}C_{z}} - {\frac{1}{2}\rho\; f_{e}w\sqrt{{u\; 2} + {w\; 2}}}}} & (1) \\{{m\;\overset{.}{u}} = {{\rho\left( {\pi\; R^{2}} \right)\left( {\Omega\; R} \right)^{2}C_{x}} - {\frac{1}{2}\rho\; f_{e}u\sqrt{{u\; 2} + {w\; 2}}}}} & (2) \\{{I_{R}\Omega\;\overset{.}{\Omega}} = {P_{S} - {\frac{1}{\eta}{\rho\left( {\pi\; R^{2}} \right)}\left( {\Omega\; R} \right)^{2}C_{P}}}} & (3) \\{\overset{.}{h} = {- w}} & (4) \\{\overset{.}{d} = u} & (5) \\{{\overset{.}{P}}_{S} = \frac{1}{\tau_{p}\left( {P_{res} - P_{S}} \right)}} & (6)\end{matrix}$where, P_(res) is the steady-state power remaining following a throttlecut during a simulated engine failure.

In Eq. (6) a first order response is assumed for turboshaft engines(Ref. 4). The coefficients are defined as:

$\begin{matrix}{C_{P} = {{\frac{1}{8}\sigma\; c_{d}} + {C_{T}\lambda}}} & (7) \\{C_{x} = {C_{T}\sin\;\alpha}} & (8) \\{C_{z} = {C_{T}\cos\;\alpha}} & (9)\end{matrix}$λ is the inflow ratio defined as (Ref. 4):

$\begin{matrix}{\lambda = \frac{{u\;\sin\;\alpha} - {w\;\cos\;\alpha} + v}{\Omega\; R}} & (10)\end{matrix}$and the induced velocity ν is approximated as:ν=K_(ind)υ_(h)f_(I)f_(G)  (11)ν_(h) is the reference induced velocity at hover defined as:

$\begin{matrix}{v_{h} = {\left( {\Omega\; R} \right)\sqrt{\left( \frac{C_{T}}{2} \right)}}} & (12)\end{matrix}$

The induced velocity parameter f_(I) is defined as the ratio of theactual induced velocity to the reference velocity ν_(h). The followingexpression is used to determine f_(I):

$\begin{matrix}{f_{I} = \left\{ \begin{matrix}{1/\sqrt{\left( {b^{2} + \left( {a + f_{I}} \right)^{2}} \right)}} & {{{{if}\mspace{14mu}\left( {{2a} + 3} \right)^{2}} + b^{2}} \geq 1.0} \\{a\left( {{{.373}a^{2}} + {{.598}b^{2}} - 1.991} \right)} & {otherwise}\end{matrix} \right.} & (13)\end{matrix}$where, a and b are defined as:

$\begin{matrix}{a = \frac{{u\;\sin\;\alpha} - {w\;\cos\;\alpha}}{v_{h}}} & (14) \\{b = \frac{{u\;\cos\;\alpha} + {w\;\sin\;\alpha}}{v_{h}}} & (15)\end{matrix}$

The term f_(G) accounts for the decrease in induced velocity due toground effect. The source model (Ref. 4) appears as:

$\begin{matrix}{{f_{G} = {1 - \frac{R^{2}\cos^{2}\theta_{w}}{16\left( {h + H_{R}} \right)^{2}}}}{{where},}} & (16) \\{{\cos^{2}\theta_{w}} = \frac{\left( {{- {wC}_{T}} + {vC}_{z}} \right)^{2}}{\left( {{- {wC}_{T}} + {vC}_{z}} \right)^{2} + \left( {{uC}_{T} + {vC}_{x}} \right)^{2}}} & (17)\end{matrix}$

The tip path plane angle α and the aircraft pitch angle θ areeffectively equivalent for the purposes of aircraft control. Thecollective pitch, computed using blade element theory (Ref. 2), appearsas

$\begin{matrix}{\delta_{c} = \frac{{\left( {1 + {\frac{3}{2}\mu^{2}}} \right)\left( \frac{6C_{T}}{a\;\sigma} \right)} + {\frac{3}{2}{\lambda\left( {1 - {\frac{1}{2}\mu^{2}}} \right)}}}{\left( {1 - \mu^{2} + {\frac{9}{4}\mu^{4}}} \right)}} & (18)\end{matrix}$

where σ and α are the rotor solidity ratio and rotor blade twodimensional lift curve slope respectively. The advance ratio μ isdefined as

$\begin{matrix}{\mu = \frac{{u\;\cos\;\alpha} + {w\;\sin\;\alpha}}{\Omega\; R}} & (19)\end{matrix}$The Optimal Autorotation Problem Formulation

A direct method of optimization was used following the work done byCarlson in Ref. 7. In the direct method the two-point boundary valueproblem is transformed into a parameter optimization problem. In such aformulation the states and controls are the parameters to be solvedsatisfying the dynamics and other physical limitations at discretepoints in time (nodes), which can be solved using standard non-linearprogramming methods and software. The direct collocation method is usedwhere both the rotorcraft states and controls are discretized throughouttime and the rotorcraft equations-of-motion are imposed as a set ofnon-linear equality constraints at each point in time (or node). Basedon the experience documented in Ref. 7, this method has a betterconvergence radius with a wider range of initial guesses (more robust toinitial guess values) than other parameterization methods. Thedisadvantage of this method is that the dimension of the problem becomeslarge due to the discretization of the states and control at each nodeor point in time. As in Ref. 8, the parameter optimization problem wassolved using the Sequential Quadratic Programming (SQP) algorithm asimplemented in the SNOPT software package (Ref. 15).

The Constraints On Solution of the Problem

(a) Equality Constraints

1. Initial Value Constraints

-   -   States: (0, u₀, Ω₀, h₀, 0, P₀)    -   Controls: (C_(T) _(o) ,α₀)

2. Final Value Constraints

-   -   States: (∞, ∞, ∞, 0, ∞, ∞)

3. Equations of Motion at each node

(b) Inequality Constraints

1. State Constraints

-   -   −w_(max)≦w≦w_(max)    -   0≦u≦∞    -   Ω_(min)≦Ω≦Ω_(max)    -   0≦h≦∞    -   0≦d≦∞    -   0≦P_(S)≦∞

2. Controls Constraints:

-   -   C_(T) _(min) ≦C_(T)≦C_(T) _(max)    -   α_(min)≦α≦α_(max)

The above constraints on states and controls are defined by

w_(max)=60 fps

-   -   Ω_(min)=0.75Ω₀    -   Ω_(max)=1.05Ω₀    -   α_(min)=−20 deg    -   α_(max)=34 deg

where, α_(min) and α_(max) are chosen as the minimum and maximum pitchvalues observed in flight test data (Refs. 16 and 17). C_(T) _(min) andC_(T) _(max) are aircraft-specific, with C_(T) _(min) associated withthe minimum collective pitch, and C_(T) _(max) associated with bladestall. Also, to impose realistic collective range, the collective boundsare implemented such that:

-   -   δ_(col) _(min) ≦δ_(col)≦δ_(col) _(max)

The conversion between δ_(col) and C_(T) has been performed via Eq. (18)and an iterative method based on trim estimation. The constraint on thepitch angle near the ground has been imposed to prevent the tail fromhitting the ground. The constraint is the function of aircraft geometry,such as the tailboom length, and altitude, and, as a result, the optimalsolution guarantees that the aircraft's tail doesn't hit the ground atthe final touchdown.

The Objective Function

The objective function is the sum of weighted penalties consisting offorward speed and sink rate at the final touchdown as well as thecontrol rates for thrust coefficients and tip path angles at each node.The minimization of control rates provides smoother and consistentbehavior of optimal solutions.

$\begin{matrix}{J = {{Q_{1}{\sum\limits_{i = 1}^{N - 1}\left\lbrack \frac{{C_{T}\left( {i + 1} \right)} - {C_{T}(i)}}{\Delta\; t} \right\rbrack^{2}}} + {Q_{2}{\sum\limits_{i = 1}^{N - 1}\left\lbrack \frac{{\alpha\left( {i + 1} \right)} - {\alpha(i)}}{\Delta\; t} \right\rbrack^{2}}} + {Q_{3}\left( u_{t_{f}} \right)}^{2} + {Q_{3}\left( w_{t_{f}} \right)}^{2}}} & (20)\end{matrix}$where, i is the node number (where i=1 is the first node at t=0) andQ_(i) represents proper weighting factors that is selective for bestperformance.

Validation of the algorithm using flight data was presented previously(Ref. 18) and showed that the optimal trajectories computed with thisformulation were reasonable when compared with those accomplished by anexpert pilot in flight tests.

The Flare Law

In real-time application for automated autorotation, performancedifferences between the rotorcraft dynamics and the point-mass modelused in the optimization as well as simulation timing issues cause amismatch in the altitude predicted by the optimization algorithm and theactual altitude of the rotorcraft (simulation, in this case). Duringinitial development it was noticed that this mismatch caused therotorcraft to flare too early or too late. To compensate for thesedeficiencies, a flare law was devised that would take over from theoptimal guidance at a pre-determined altitude near the ground and flarethe rotorcraft based on a more conventional compensatory control law. Inpractical terms, this flare law attempted to recreate the final flareand landing performed by a pilot based on outside visual cues. Thepurpose of the optimal trajectory was to bring the rotorcraft to apre-flare altitude at an energy condition that was conducive to a safeflare and landing.

The flare law is preferably activated at a height of approximately 30 ftabove ground and uses a non-linear algorithm to modulate airspeedthrough rotorcraft pitch attitude and to modulate rotor-speed andsink-rate through collective control. The activation altitude requiredsome adjustment during development and evaluation to compensate for thevariations in aircraft weight.

Brief Description of the Simulator

Development and evaluation of the automatic autorotation andautorotation flight director display of the present invention took placeon a commercial helicopter Flight Training Device (FTD) manufactured byFrasca International, Urbana, Ill. Although not officially certified,the FTD used for the evaluation incorporated a level of fidelitynecessary for achieving FAA Certification as a Level 4 FTD. The FTD wasa fixed-base simulation of a Bell-206L-4 single-turbine, single rotorhelicopter (FIG. 1) with a realistic reproduction of the cockpit with aframe and dual controls and a dome visual system with 180-deg horizontaland 60-deg vertical visual field-of-view (FIG. 2). An additionalgraphics channel provided visual imagery immediately below the cockpitdoor and through the chin window on the pilot's side. The cockpitcontrollers were replicas of the actual cyclic, collective and pedalcontrols and had realistic feel.

Complete engine failures could be triggered from the simulatoroperator's station at any time. Engine failures resulted in immediateloss of all engine power and the activation of appropriate warninglights and audio alarms. A low-rotor RPM warning light was alsoprovided. The rotorcraft simulation model was a rotor disk model withaerodynamic models for the fuselage and empennage surfaces. Therotorcraft model had previously been evaluated by line pilots as part ofthe FTD acceptance testing and found to be representative of the actualaircraft in the regular and autorotation flight regimes. The primarydevelopment pilot for this project, Ed Bachelder, an experiencedhelicopter pilot (SH-60B pilot) also found the rotorcraft simulation tobe realistic.

Implementation of the Optimal Guidance Algorithm

With reference to FIG. 3, a block diagram indicates how a laptoppersonal computer (PC) running the real-time optimization algorithm waslinked with the Frasca simulation computer.

The PC used for the development and evaluation of the optimal guidancewas a conventional commercial laptop PC with a 2 GHz Intel Pentium®processor and a Windows 2000® operating system. The PC acceptedrotorcraft state and control information at a nominal 30 Hz data rateand output collective, cyclic, and pedal control positions to thesimulation computer, also at a 30 Hz data rate. Communication wasfacilitated through an Ethernet link using standard Microsoft Windowscompatible communication protocol. During powered flight, the optimalalgorithm continuously updated the optimal solution based on therotorcraft states (primarily speed and altitude) being received from thesimulation computer. In effect, the optimizer continuously computed anupdated optimal trajectory for autorotation with the assumption that anengine failure had just occurred. Typically, a new update was availableevery 3 sec or sooner. Initially, when an engine failure occurred, theautomatic autorotation guidance was based on the last optimal trajectoryupdate that was available. As presently implemented, the optimaltrajectory is updated throughout the autorotation maneuver. The optimalguidance algorithm considers only the optimal trajectory in thelongitudinal axis (collective and longitudinal cyclic commands only).During the development and evaluation process a simple compensatoryfeedback control was implemented to maintain roll attitude and headingvia lateral cyclic and pedal commands.

During the development and evaluation process a guidance display wasgenerated on the laptop computer to provide an indication of how wellthe helicopter was following the optimal guidance during automaticautorotations. For piloted operations of actual working aircraft, suchas with a remote operator, the display is used as a flight director toguide the operator on the optimal control timing and magnitude inputsrequired to accomplish a safe landing. The guidance display includes anovel display concept that guides a human operator in following andperforming the optimal control inputs by providing a preview of thecomplete trajectory.

The primary intent of the development and validation of the optimalguidance algorithm in this real-time simulation environment was toevaluate the robustness of the guidance algorithm across the flightenvelop of the simulated helicopter. Invariably, however, emphasis wasplaced on the “worst case” flight conditions; i.e., entry intoautorotation from flight conditions that are well within the “avoid”region of the height-velocity diagram for this helicopter (shown in FIG.4) as these clearly illustrate the benefit of the optimal guidanceprovided by the present invention. Development and refinement of theoptimal guidance algorithm and its real-time mechanization at flightconditions within the “avoid” region of the H-V diagram also maximizesthe probability that the guidance provided by the present invention willenable safe autorotations from flight conditions outside the avoidregion. The majority of the development and evaluation of the optimalguidance and the flight director display was performed at a vehiclelight-weight condition with limited evaluations at the vehicle heavy(maximum gross weight) and medium weight conditions.

The optimal control algorithm uses a simple point-mass type model forthe rotorcraft. For the algorithm to provide appropriate autorotationguidance, therefore, it was necessary to fine-tune the point-mass modelparameters such that the dynamics and performance of the point-massmodel approximated the rotorcraft model as implemented in the simulatoras closely as possible. For automated autorotations, it was particularlyimportant to scale and bias the optimal control inputs computed by theoptimal algorithm so that it would be able to backdrive the simulationcorrectly. An automated procedure was setup using Matlab® to facilitatethis parameter optimization process using rotorcraft state and controltime history data obtained from the simulator.

The Simulator Results

Following three-week period of development on the Frasca FTD in Urbana,Ill., the automatic autorotation capability was refined to an extentthat allowed evaluation of the algorithm over a range of autorotationentry conditions. The entry conditions that were attempted at light(2900 lbs), medium (3500 lbs), and heavy (4450 lbs) vehicle weightconfigurations using the automatic autorotation guidance are presentedon a height-velocity diagram in FIG. 5. The manufacturer'sheight-velocity “avoid” regions are indicated in FIG. 5 by dashed lineslabeled for the rotorcraft's weight. Successful landings are shown asopen or clear symbols and crash landings are shown as solid or filled 1symbols. Crash landings represent those where the touchdown sink-rate orforward speed exceeded the manufacturer's specified limitations for therotorcraft. Tail-strikes were also counted as crash landings. Thedetermination of a safe or crash landing was made by the Frascasimulation software.

As may be observed with reference to FIG. 5, it is clearly establishedthat using the optimal guidance of the present invention, safeautorotations are possible from well inside the “avoid” regions of theH-V curve including the high-speed region. Fewer evaluations wereconducted at the medium and heavy vehicle weight conditions. At theheavy and medium vehicle weight conditions, it is expected that refiningthe constraints (rotor-speed and vertical speed limits, for example) aswell as the flare law parameters would have allowed greater success thanwas demonstrated during the course of development and evaluation of thealgorithm. Nevertheless, safe landings were accomplished at these weightconditions from well within the “avoid” regions of the H-V curve forthese weights, although not with the consistency that was achieved atthe light-weight condition.

The touchdown sink-rates and forward speeds for all the automatedautorotation entry conditions shown in FIG. 5 are presented in FIG. 6(light-weight condition) and FIG. 7 (medium and heavy weightconditions). FIGS. 6 and 7 indicate that, in most situations, touchdownconditions were well within the limitations of the rotorcraft. Almostall the landings were accomplished with some forward velocity. This isespecially true in the heavy and medium weight conditions. This isprimarily due to the use of the flare law for the landing. Examinationof the optimal solutions for these evaluations indicated that if thehelicopter had been landed using the optimal algorithm (assuming theaforementioned technical difficulties were resolved), the forwardvelocities at touchdown would have been reduced.

Selected representative time histories for the automated autorotationsare presented in FIGS. 8, 9, 10, and 11 for the light weight conditionand FIG. 12 for the heavy-weight condition. In each of these examples,the engine is failed at time t=0 and the displayed time history is endedwhen touchdown is registered by the simulation computer. FIGS. 8 and 9demonstrate the extreme nature of the maneuver that is required whenautorotating from a hover at 200 ft and 400 ft altitude (above groundlevel). FIGS. 8 and 9 demonstrate that it is possible to autorotatesafely from well within the avoid region of the H-V curve, if thecontrol inputs are well-timed and of appropriate magnitude. At the lowerentry altitude (FIG. 8), immediate nose down pitch attitude ofapproximately 30 degrees is commanded whereas collective is lowered tozero over a period of roughly 3 sec following engine failure. A pitchpull-up is commenced at an altitude of approximately 100 ft continuinginto a landing flare using pitch attitude and collective input atapproximately 50 ft altitude. The sharp discontinuity in thelongitudinal cyclic at approximately 50 ft altitude marks the transitionfrom the optimal algorithm to the flare law. Rotor speed is maintainedabove 80% throughout most of the maneuver with rotor speed reducing to60% at touchdown as rotor speed is sacrificed to reduce the touchdownsink rate. No attempt was made to refine the algorithm to smoothlytransition between these modes, hence the sharp discontinuity.Modification of the algorithm and/or the flare law to smooth thetransition between these modes is within the skill of one of ordinaryskill in the art and is within the scope of the present invention.

With reference to FIG. 8, the longer maneuver time allowed by the higherentry altitude is evident. The collective is lowered immediately butthere is no command to push the nose over or pitch down and gainairspeed until the rotor-speed approaches its lower constraint of 75%.To maintain rotor speed above the constraint of 75%, the optimalguidance algorithm trades altitude for airspeed and for maintainingrotor speed. With reference to FIG. 9, a maximum nose-down pitchattitude of 40 degrees is observed. A run-on landing is achieved at aforward speed of approximately 20 kts and a touchdown sink rate ofalmost zero.

FIG. 10 demonstrates the effectiveness of the optimal guidance algorithmfor an entry condition in the high-speed “avoid” region of the H-Vcurve. Due to the low altitude, the flare law almost immediatelyoverrides the optimal algorithm. The helicopter is commanded to pitch upand trades airspeed for rotor-speed and altitude, placing it in asuitable energy state for a safe flare and touchdown at a forward speedof less than 10 kts. FIG. 11 demonstrates an autorotation from an entrycondition that is outside the manufacturer's recommended avoid region ofthe H-V curve for the light-weight condition. In response to the optimalguidance commands, the helicopter initially pitches nose-up to reduceairspeed followed by nose-down pitch to gain airspeed and maintain rotorspeed above the constraint limit of 75%. Touchdown is achieved at a sinkrate of 3 ft/sec and a forward speed of 40 kts.

The capability of the automatic guidance algorithm of the presentinvention to safely autorotate for the heavy-weight condition isdemonstrated in FIG. 12. The engine is failed when the helicopter is ata hover at an altitude of 400 ft above ground. When contrasted with anautorotation from a similar entry condition for the light-weightcondition (FIG. 9), the helicopter sinks more rapidly resulting in ashorter flight time. The optimal guidance commands an almost immediatepush-over to gain airspeed (contrast with almost no pitch input forseveral seconds in FIG. 9) and maintain rotor-speed with a very rapidpull-up to about 35 degrees to arrest sink rate at low altitude. Thepull-up results in the rapid increase in rotor-speed to approximately100% which is traded-off for sink-rate reduction using collective.Touchdown is achieved at a sink rate close to zero and a forward speedof 27 kts. As would be expected the heavier weight conditions proved toleave very little room for computational or timing errors.

The appropriately formulated optimization algorithm of the presentinvention may be used to provide autorotation guidance in real-time to arotorcraft. This “automated autorotation” capability is beneficial onunmanned rotorcraft where redundancy for failure management is notnecessarily a primary design requirement. The present optimal guidancemethod has demonstrated a repeatable capability to safely autorotate ahelicopter from a variety of entry conditions and a range of weights,even when these entry conditions are well within the avoid region of theheight-velocity diagram.

Display Implementation

The present invention relates to a human-operator cueing and trainingmethodology using optimal control for application to the time criticalmaneuvering of dynamic systems including vehicles. The methodology canalso be used for automated guidance of dynamic systems through timecritical maneuvers. The description of the invention uses a particularapplication example of rotorcraft pilot training and automatic guidance.FIG. 13 illustrates the invention when applied for training rotorcraftpilots on autorotation and reduced-power flight using a flightsimulator. In this application (FIG. 13), a standard PC with theinvented system installed is linked with a flight simulator and acceptsrotorcraft state and control information from the connected flightsimulator. Communication uses an Ethernet link using standard MicrosoftWindows compatible communication protocol. During powered flight, theoptimal algorithm continuously updates the optimal solution based oncurrent rotorcraft states being received from the simulation computer.Thus the optimizer continuously computes an updated optimal trajectoryfor autorotation with the assumption that an engine failure had justoccurred. Typically, a new update is available within a couple ofseconds. When an engine failure occurs, the automatic autorotationguidance is based on the last optimal trajectory update that wascomputed. The optimal algorithm considers only the optimal trajectory inthe longitudinal axis (collective and longitudinal cyclic commandsonly).

FIG. 14 describes the software implementation of the optimal algorithmas a flowchart. The software starts with initializing all necessaryrotorcraft parameters and setting all necessary constraints and costs tocompute the optimal controls. The parameters are vehicle specific sothat they can be adjusted for different vehicles and dynamic systems—arotorcraft in this application. Next, the current flight conditions aswell as the current environmental information such as wind, weightchanges, and atmospheric temperature changes to computes air density areread into the software. The rotorcraft collective control input positionfrom the flight simulator is converted to thrust that is used in therotorcraft dynamic model to compute optimal controls. The software alsoestimates the best guess values of optimal controls to facilitate thecomputation of the optimal guidance solution. After the softwarefinishes the computation, it converts the optimal thrust solution tocollective and cyclic control inputs that can be displayed on theguidance display.

A guidance display is also generated on the PC that provides a previewof the optimal control solution with time and facilitates tracking ofthe optimal solution by the pilot through the maneuver. To learn theoptimal control inputs necessary for safe recovery from the power-lossor reduced-power situation, the pilot simply has to track the guidancelines as discussed below. Repeated flights on a flight simulator usingthis guidance will provide the pilot with a clear understanding of thecontrol inputs and rotorcraft trajectory to be flown for safe recovery.FIG. 15 illustrates the guidance display.

With reference to FIG. 15, the rotorcraft or helicopter symbol (1) isdenoted by a stylized graphic intended to be readily recognized as aside view of a helicopter and the key aircraft states are anchored tothis symbol to facilitate rapid mental processing as the symbol moves onthe display. The helicopter symbol (1) also pitches with the helicopterpitch. The dimensions of the helicopter symbol (1) are drawn to scalewith the altitude axis so that the pilot can see when tail contact isimminent and the relation between tail height and pitch.

With further reference to FIG. 15, the helicopter tail acts as a pointerto the radar altimeter readout (2). The radar altimeter readout (2) ispreferably positioned behind or aft of the helicopter symbol (1) on thedisplay. A series of short horizontal lines arrayed vertically orstacked below the helicopter symbol (1) is an altitude pipper or heightabove ground markers (3) which indicate the height-above-ground by shorthorizontal lines or markers corresponding preferably to heights of 150,80, 40, 20, 10, and 0 feet. If the helicopter is above 150 feet (as inFIG. 15), the helicopter symbol (1) will remain fixed at the 150 feetmarker until the altitude goes below 150 feet, at which point thehelicopter symbol (1) begins descending. A rotor speed indicator (4)includes a rotary pointer and digital readout box that is positionedabove the helicopter symbol (1). The rotor speed indicator (4) changesfrom steady to blinking if the rotor speed falls below 90% or risesabove 110%. A forward speed indicator (5) emanates and extends as a(body-axis referenced) vector from the nose of the helicopter symbol(1). The length of the vector (5) is in direct proportion to the forwardspeed of the helicopter. The forward speed readout in knots is tagged tothe head of the forward speed indicator vector (5). A vertical speedindicator (6) vector (ground referenced) emanates and extends verticallydownward from the tail of the helicopter symbol (1). The vertical speedvector (6) originates from the tail since this is the natural point ofinterest for that state. The forward and vertical speed vectors areshown in FIG. 15. The scales on the vertical and forward speeds areidentical and dimensioned with respect to the radar altimeter (i.e., 10fps corresponds to a 10 foot increment on the altimeter (2)). The tickson the vertical speed vector correspond to 5 fps, while on the forwardspeed bar ticks denote 10 knots increments. It is to be noted that thelengths of these vectors are scaled so that the pilot can weigh themequally. When the vertical speed vector touches the ground referencemarker (attitude pipper), there is one second remaining prior to tailcontact (based on the current vertical speed), at which time the pipperblinks in intensity to alert the pilot of the impending contact. Thisunique feature results from the scaling chosen, allowing the pilot torefine control timing.

With continued reference to FIG. 15, a collective range settingindicator (7) scale is positioned on the display to the left of thealtitude pipper or height above ground markers (3). The white ticks onthe collective indicator (7) denote the 0% and 100% collectivepositions. The rotor blade stall limit indicator (8) (red bar) shows thecollective setting corresponding to the blade stall limit at thatparticular point in time, and it varies considerably throughout theautorotation. The collective range setting indicator (8) movescorrespondingly with the collective inputs from the pilot. Aleft-pointing triangle (9) positioned below the altitude pipper (3) andto the right of the collective indicator (7) points to and tracks thecurrent collective position. If this collective tracker pointer (9)nears or exceeds the rotor blade stall limit, it will change from asteady preferably white color to blinking alternating colors to alertthe pilot that lift will be lost. One aspect of the maneuver that isalmost never considered in autorotation training is the stall limit(presumably because one can't see it or predict it with the standardinstrument layout), but it easily exceeded, to the detriment of themaneuver. This limit is predicted based on the point-mass helicoptermodel. The pointers are fixed in the display to allow the pilot bettertracking. The collective range indicator moves with the collective inputfrom a pilot so that the pilot can have a clear idea of his currentcollective input and the overall possible range of collective movements.A right-pointing triangle (10) positioned below the altitude pipper (3)and to the right of the collective tracker pointer (9) points to andtracks the current pitch position. The white right-pointing trianglebelow the altitude pipper points to the current pitch position. Forexample, the pilot should follow the pitch commands displayed in FIG. 15with the pitch tracker pointer (10). Time marks (11) are displayed onthe optimal collective and pitch commands as tick marks for every secondto give a pilot a better preview of overall profiles and the anticipatedtime remaining to complete maneuver.

Referring further to FIG. 15, the sideslip indicator (12) is shown belowthe attitude pipper as a ball referenced to a fixed vertical centerline.The sideslip indicator ball will move to the right or left with respectto the nominal centerline in response to corresponding sideslip. Theengine turbine speed indicator (13) is shown on the upper right of thedisplay as a rotary pointer and digital readout box for displayingpercent of turbine maximum speed. Guidance commands to the collective(left white line) and pitch (right white line) are displayed as timeprofiles for the collective director (14) command suite and pitchdirector (15) command suite, with a time tick for every second. Thecontact points with the collective and pitch pointers represent thepresent time or time equal to zero. The command profile lines indicatethe anticipated time to complete autorotation in seconds. These profilelines move in time so that the collective command profile scrolls rightand the pitch command profile scrolls towards the left. The pilot mustmove the controls to minimize the vertical separation between thecurrent control setting (left collective tracker pointer (9), rightpitch tracker pointer (10)) and the coincident command. A crucialadvantage that the present display has over the more traditional flightdirector is that the pilot is given a highly usable view of futurecontrol motion and time. Using this preview the pilot can anticipatecontrol motion as well as anticipated time to complete maneuver, whichis critical to precise and timely control tracking. The optimal commandswill change from steady color to blinking with a different color whenthe “auto flare law” would be activated if the autopilot mode were inuse. In this way, a pilot will be alerted to prepare for the landingflare. The color of the optimal commands change to denote the quality ofoptimal solutions. Due to the rapid changes of entry conditions andnumerical complexity associated with the optimization algorithm theoptimal solution might not have converged. In this case, the optimalcommands change color to indicate that the commands are not based on aconverged solution, in which case the displayed commands are from thelast solution that converged.

FIG. 16 illustrates the application of the invention to automaticcontrol of a vehicle or dynamic system (a rotorcraft in the exampleapplication). The implementation is similar to that indicated in FIG. 13except that the optimal control solutions are fed back to the flightsimulator or actual vehicle and used to replace the normal controlinputs. The optimal solution will then guide the simulator or actualvehicle to a safe recovery from the power-loss or reduced-powersituation. When acting as an automatic guidance and control system, acompensatory feedback control law is also implemented to maintain rollattitude and heading via lateral cyclic and pedal commands and thesystem sends the optimal control commands to the simulator to drive thesimulator for safe landing in autorotation. A separate flare algorithmtakes over near the ground to compensate for possible differences in therotorcraft dynamics between the system and the simulator.

FIG. 17 illustrates the application of the invention to a computer-basedtraining device for rotorcraft autorotation and reduced-power emergencyflight situations. The basic operation of the algorithm follows thatdepicted in FIG. 14 except that there is no connection with a simulationor flight vehicle. The optimal solution is displayed to the traineepilot and the simulated rotorcraft together with a computer-generatedscene of the pilot's view out of the rotorcraft. When activated by thetrainee pilot, the simulated rotorcraft follows the computed optimaltrajectory, providing the trainee pilot with an understanding of therotorcraft attitudes, path and control inputs necessary for saferecovery. The software will allow the trainee pilot to adjust therotorcraft initial and final conditions and examine the effect of theseconditions on the optimal solution.

In order to give the pilot proficiency at entering the autorotationprofile, simulated engine failure is initiated at various altitudes,airspeeds, and horizontal locations relative to a geographically fixedlanding site. This will exercise the full envelope of entry conditionswithout the pilot having to indicate to the computer the intended pointof touchdown. The display also may be used as an on-board pilot previewof the optimal autorotation maneuver strategy. As the helicopter readiesfor departure from a hover, the autorotation computer will begincomputing the optimal inputs and display them. The pilot would includethe display in his instrument scan so that if the engine were to fail atany given time an image of the control profile would be mentallyavailable. The entry into the autorotation would therefore be executedprecognitively, followed by scanning of the autorotation display andcockpit instruments during the steady-state phase (if there is one) andjust prior to the flare. In instances where out-of-balance flight isrequired, (to prevent site overshoot, rotor overspeed, or to compensatefor other conditions) the pedal control profile will commandappropriately so that the pilot may develop skill in slipping thehelicopter according to the situation.

The training display concept of the present invention where the operatoris provided with visual cues on where to place the controls at thecurrent instant as well as provide a preview of where the controlsshould be in the future (based on the optimal algorithm) has applicationto any vehicle or device that requires time-critical inputs for safeoperation. Employing trajectories and control inputs using constrainedoptimization can be applied to any vehicle or device that requirestime-critical inputs for safe operation.

The concepts, algorithms and routines for implementing the real-timedynamic visual display methodology of the present invention are furtherdisclosed and described in the following Table 1 which providesrepresentative examples, in a common programming language, of computercode capable of implementing the primary portions, but not the entirety,of the visual display of the present invention in a suitable computerprocessing environment. Table 1 is a listing of the computer code forthe DrawDisplay.CPP display guidance-commands and flying informationroutine of the Guidance-Commands Display and Communication Module of thecomputer implementation of the present invention.

The scope of the appended claims will be clear from the entirety of thepresent disclosure. It will be obvious to those of ordinary skill in theart that the concepts, algorithms and displays of the present inventionmay be implemented in alternative code formulations and/or in otherprogramming languages and such alternative formulation or formulationsare within the scope of the present invention.

Thus, a real-time trajectory optimization method for guiding arotorcraft in the event of loss of engine power is described inconjunction with one or more specific embodiments. The invention isdefined by the following claims and their full scope of equivalents.

1. A computer implemented method for guiding a pilot of a rotorcraft insimulated autorotation from a current state of simulated flight having aconstrained optimal trajectory for autorotation to landing comprisingthe steps of: (a) determining the current state of the rotorcraft; (b)executing a guidance algorithm to compute the current constrainedoptimal trajectory of the rotorcraft for autorotation to landing; (c)executing the guidance algorithm to compute inputs for rotorcraftcollective and pitch controls required to achieve the current optimaltrajectory; (d) providing a visual guidance display including: (i) asymbol for the rotorcraft indicating the current pitch of therotorcraft; (ii) a symbol representative of collective control positionrequired to achieve the current optimal trajectory; (iii) a symbolrepresentative of the current collective control position; (iv) a symbolrepresentative of the pitch control required to achieve the currentoptimal trajectory; and (v) a symbol representative of the current pitchcontrol; (e) providing the pilot visual cues where to currently positionthe collective control and the pitch control to follow the currentoptimal trajectory; (f) providing the pilot a visual preview of when andwhere to position the collective control and the pitch control at futuretimes to follow the current optimal trajectory; (g) repeating steps (b)through (e) until landing occurs.
 2. A helicopter guidance system forlanding a simulated airborne helicopter following a partial or totalhelicopter engine power failure comprising: (a) state input signalsrepresentative of a current state of the helicopter; (b) control inputsignals representative of a current set of controls for the helicopter;(c) a helicopter guidance algorithm; (d) a computer adapted to; (i)receive the state input signals; (ii) receive the control signals; (iii)execute the guidance algorithm to compute an optimal current trajectoryfor a simulated landing of the helicopter; (iv) execute the guidancealgorithm to compute current trajectory output signals representative ofthe optimal current trajectory; (v) execute the guidance algorithm tocompute a set of current controls positioning required for the simulatedairborne helicopter to achieve the optimal current trajectory; and (vi)execute the guidance algorithm to compute controls positioning outputsignals representative of the controls positioning required to achievethe optimal current trajectory; and (e) a visual guidance displayincluding: (i) a symbol for the helicopter; (ii) indicators of the stateof the helicopter; (iii) indicators of the controls positioning of thehelicopter; (iv) indicators of control inputs required to achieve theoptimal current trajectory; (v) visual cues for positioning of controlsnecessary to achieve the optimal current trajectory; and (vi) indicatorsof future positioning of controls required to achieve the optimalcurrent trajectory.
 3. The helicopter guidance system of claim 2 inwhich the symbol for the helicopter is a representation of a side viewof the helicopter and of the head and of the tail of the helicopter. 4.The helicopter guidance system of claim 2 in which the indicators of thestate of the helicopter are anchored to the symbol for the helicopter.5. The helicopter guidance system of claim 2 in which the symbol for thehelicopter is adapted to pitch with the pitch of the helicopter duringlanding.
 6. The helicopter guidance system of claim 2 further includinga series of horizontal lines representative of an altimeter readout asone of the indicators of the state of the helicopter.
 7. The helicopterguidance system of claim 2 further including a rotary pointer andnumerical display as indicators of the helicopter's rotor speed.
 8. Thehelicopter guidance system of claim 3 further including a variablelength vector extending from the symbol of the helicopter head as one ofthe indicators of the helicopter's forward speed.
 9. The helicopterguidance system of claim 3 further including a variable length vectorextending from the helicopter tail as one of the indicators of thehelicopter's vertical speed.
 10. The helicopter guidance system of claim2 further including a collective range setting indicator scale and acollective indicator as indicators of the position of the collectiverelative to 0% and to 100% collective positions.
 11. The helicopterguidance system of claim 10 further including a rotor blade stall limitindicator corresponding to the helicopter's rotor blade stall limit. 12.The helicopter guidance system of claim 2 further including a time linerepresentative of collective guidance commands for collective positionover time as one of the indicators of control inputs required to achievethe optimal current trajectory.
 13. The helicopter guidance system ofclaim 2 further including a time line representative of pitch guidancecommands for pitch position over time as one of the indicators ofcontrol inputs required to achieve the optimal current trajectory.